1. Field of the Invention
The present invention relates to the control of electrical loads, such as for example, high-efficiency lighting systems and motor systems. More particularly, the present invention relates to a method and apparatus for controlling an electrical load exhibiting destabilizing negative resistance negative damping characteristics to provide positive damping of power grid oscillations and for controlling the electrical load to operate at a reduced power level when the power grid voltage is reduced.
2. Description of the Related Art
The quest for ever higher energy efficiency is being pursued with little concern for the resulting impact on stability of the power grid. The power grid has an ever-increasing tendency to become unstable and oscillate.
FIG. 1 presents a 0.5 Hz ringing transient waveform that has a damping ratio of five percent. Transient waveforms of this sort are observed frequently on the power grid. Although a system that has such a transient response would be classified as stable, it is clear from the ringing nature of the waveform that the power grid has a very poor margin of stability. Waveforms of this sort are judged as being a “cause for concern” if the degree of damping is five percent or less and judged as being a cause for remedial action if the degree of damping is three percent or less.
The waveform of FIG. 1 is intended to represent the power grid transient response as observed in the synchronous reference frame, wherein the observer would be revolving at synchronous speed and observing the generator shaft angle advance and retard relative to the synchronous speed undisturbed reference position. A similar observation could be made using a stroboscope to view an index mark on the generator shaft. The existing and growing tendency toward oscillatory instability is a very substantial cause for concern. Establishing five percent damping as the threshold of “cause for concern” is simply a necessary act of triage. In the interest of energy efficiency, we are replacing loads that have a stabilizing effect, such as electric water heaters, electric resistance heating, incandescent lamps, and inductive ballast fluorescent lamps, with destabilizing loads, such as heat pumps, high power-factor fluorescent ballasts and light-emitting diode (LED) drivers. Considering the current state of marginal stability, it appears likely that the power grid soon will become dysfunctional as a result of more frequent instances of oscillatory instability unless the present design philosophy related to power system loads is modified.
For lighting systems, the related art involves flicker, incandescent lamps, fluorescent lamps employing conventional inductive ballasts, compact fluorescent lamps, LED lighting, modern high-efficiency high-power-factor electronic ballasts and LED drivers. For motor systems, the related art involves motors and variable speed drives (VSD). For all of these systems, the related art involves constant power loads, energy efficiency, the Synchrophasor system and oscillatory instability of the national power grid(s.
Suppressed-carrier methods of measuring small-signal incremental impedance characteristics, that determine the effect that system loads have on damping of power grid oscillation, are also involved. Suppressed-carrier measurement methods involve stimulus injection and response extraction. Stimulus is provided by quadrature axis and/or direct axis modulation of the mains voltage, injection of a quadrature axis and/or direct axis suppressed carrier stimulus voltage, or injection of a quadrature axis and/or direct axis suppressed carrier stimulus current. Response extraction involves quadrature axis and/or direct axis demodulation of response signals that result from the stimulation. Suppressed carrier impedance is determined by the ratio of a demodulated response voltage and a demodulated response current. The methods produce a Nyquist diagram from the ratio of two demodulated response voltages or two demodulated response currents, from which the margin of stability may be determined from the minimum return difference, or the less exact method of gain margin and phase margin. Suppressed carrier measurement methods are described in more detail in U.S. Pat. Nos. 7,508,224 B2 and 8,044,672. Oscillatory instability of AC powered systems tends to occur in modulation sidebands spaced symmetrically about the mains frequency. Hence, the label suppressed carrier. The mains frequency component simply supplies the quiescent power that permits the oscillation to occur.
A constant-power load characteristic causes the line current to increase when the line voltage is decreased and to decrease when the line voltage is increased, thereby resulting in a negative resistance, regenerative quality that contributes negative damping of power grid oscillations. A constant-power characteristic also prevents load shedding from occurring when the grid voltage is reduced, such as during a deliberate brown out. The low-frequency per-phase input impedance of a constant power load is presented in EQ.1.RCP=−VIN2/PIN  EQ.1
Where: VIN=the rms mains voltage, line-to-neutral                PIN=the per-phase input power.        
Incandescent and fluorescent lighting consumes approximately 22 percent of the electrical energy produced in the United States, according to U.S. Lighting Market Characterization, Vol 1: National Lighting Inventory and Energy Consumption Estimate, Final Report, September 2002, DOE EERE. Because the installed base lighting consists primarily of incandescent lamps and fluorescent systems utilizing older inductive ballasts, it has a significant positive damping characteristic. Unless the current design philosophy is modified, the lighting load will be converted to use high-efficiency electronic ballasts, or LED drivers that have a constant-power characteristic. The high-efficiency lighting would then consume an estimated 14 percent of energy produced, but it would have a negative damping characteristic. Converting 22 percent of the total grid load from positive damping to 14 percent negative damping would be devastating.
Legislative action has been taken at the federal level to phase-out incandescent lamps in favor of more energy efficient lighting. Older fluorescent lamps, such as the T12 are being replaced with more energy efficient T8 and T5 lamps. Older inductive fluorescent ballasts, that have poor power factor, are being replaced with modern electronic ballasts that offer higher efficiency and very high power factor. LED lighting is replacing fluorescent lighting in commercial and industrial applications because of lower maintenance cost and is expected to be used widely in residential applications as LED systems are further developed and prices are reduced. LED technology is beginning to mature. A wide variety of LED driver controller integrated circuits is becoming available. A review of currently available electronic ballasts and LED drivers indicates that lighting systems employing these drivers will have a constant power negative resistance negative damping characteristic.
There are substantial functional and economic benefits to be derived by replacing older incandescent and fluorescent systems with more efficient lighting systems that employ more efficient electronic ballast, more efficient fluorescent lamps and highly efficient LED's and LED drivers. The high efficiency, high power factor and very low harmonic current characteristics obtainable with modern electronic fluorescent ballasts and LED drivers are highly desirable. Older inductive fluorescent ballasts have a poor power factor. However, they provide significant positive damping. The compact fluorescent lamp (CFL) employs electronic ballast that has a poor power-factor and produces significant harmonic distortion in the line current. Measurement of the impedance characteristics of four different brands of CFL's indicated that some brands have a weak negative resistance quality whereas others have a weak positive resistance quality. The net effect of a combination of all brands is estimated to form a constant current load that has no impact on damping. The primary concern, regarding replacement of incandescent lamps with CFL's, is the loss of damping provided by the incandescent lamps that are being replaced. Because of toxic mercury content, compact fluorescent lamps will probably soon be replaced by LED, or other high efficiency lighting.
Although incandescent lamps have a resistive impedance characteristic, the nonlinear nature of these lamps causes the damping effect to be only fifty-five percent of that provided by a Watt equivalent resistor. The degree of damping, provided by incandescent lamps, is determined by the incremental resistance of their filaments. An elegant mathematical characterization of incandescent lamps, operating over a range of applied voltage, has been developed and is attributed to Welch Allyn Inc., Fink and Beaty. EQ.2, EQ.3 and EQ.4 are a subset of the equations, and are set forth below. The complete set is available on the internet at http://en.wikipedia.org/wiki/Lamp_rerating. The availability of these equations greatly facilitates the understanding and quantification of incandescent lamp behavior. EQ.5 is not included in the complete set, but may be derived from EQ.2 or EQ.4, and is set forth below. In the course of deriving EQ.5 from both EQ.2 and EQ.4, it becomes apparent that the exponents in EQ.2 and EQ.4 should be related such that the exponent in EQ.4 will be equal to the exponent in EQ.2 plus 1.0. In EQ.4, the exponent has been changed from 1.6 to 1.55. This change is arbitrary, but it resolves the apparent conflict and produces a result that closely matches the incremental resistance values measured with the samples used in the course of the present work. It must be noted that EQ.2, EQ.3, EQ.4 and EQ.5 represent performance under static conditions. The thermal time-constant of the lamp filament causes a pole-zero roll-off response as the modulation frequency of the line voltage is increased.
Va≡Applied voltage
Vd≡Design voltage
Ia≡Current at applied voltage
Id≡Current at design voltage
La≡Luminous intensity at applied voltage
Ld≡Luminous intensity at design voltage
Pa≡Power at applied voltage
Pd≡Power at design voltage
Ri≡Incremental resistance at applied voltageIa=(Va/Vd)0.55×Id  EQ.2La=(Va/Vd)3.45×Ld  EQ.3Pa=(Va/Vd)1.55×Pd  EQ.4Ri=((VdN)/(N×Id))×(Va1-N) where N=0.55  EQ.5
FIG. 2 presents the suppressed-carrier impedance of a combination of one 100 Watt and one 60 Watt lamp that forms a 160 Watt incandescent lamp, operating at 120 Vrms, over a modulation frequency span of 0.1 Hz to 30 Hz. The measurements indicate that the incremental impedance of the sample incandescent system, at a modulation frequency of 0.1 Hz, is 166 Ohms. This value agrees closely with the 161 Ohm theoretical value implied by EQ.5. The near zero degree phase angle at low frequencies confirms the positive resistance positive damping characteristic, as would be expected. In the frequency region above approximately 1 Hz, the impedance reduces rapidly. Reduction of the impedance is attributed to the thermal time-constant of the incandescent filament. The phase angle lags in this frequency region in a manner that is similar to that of a pole-zero lag-lead filter.
FIG. 3 presents the flicker susceptibility of the 160 Watt incandescent lamp. Flicker susceptibility places a limit on the degree of positive damping that can be realized via modification of modern high-power-factor electronic ballast and LED drivers. The ubiquitous incandescent lamp is used, herein, as the flicker performance standard in establishing the degree of flicker susceptibility that would be acceptable. For flicker susceptibility tests, the network analyzer measures the transfer function between the network analyzer Source signal, that is used to amplitude modulate the mains voltage, and the output of a selenium photocell that is placed appropriately to measure the light output of the lighting system under test. All extraneous light is blocked to ensure that the photocell output is zero with the lighting system under test turned off. With zero modulation of the mains voltage, the photocell is positioned at a distance from the light source to cause the output of the photocell to be equal to 50 my, that is equivalent to approximately 840 Lux. The photocell employed was removed from a Yokogawa YEW 3281 LUX Meter and was terminated with a 383 Ohm resistor to simulate the loading of the YEW 3281 scale attenuator in the 1000 Lux range. This photocell configuration eliminates the motor-generator effect of the analog meter movement of the YEW 3281 LUX meter that would respond to Lux modulation and cause error. It also provides an output of 50 mV, that is substantially larger than the signal that would be available at the Lux meter terminal posts. For comparative flicker susceptibility tests, scale factors are not important. The primary intent is simply to compare flicker susceptibility of a given lighting system with that of the incandescent system. By adjusting the position of the photocell to provide a 50 mV output for any lighting system under test, flicker susceptibility of the system being measured may be done by simply comparing the resulting Source frequency component of the photocell output with that produced by the incandescent system.
FIG. 4 presents the IEEE 141 Flicker Threshold that establishes a limit on allowable periodic square-wave amplitude modulation of the mains voltage. For sinusoidal amplitude modulation, the amplitude limit can be increased by approximately 2 dB. Human sensitivity to lighting flicker varies with frequency and is the most sensitive in the region near 12 Hz. Lighting flicker is undesirable. Flicker can be annoying to human observers and excessive flicker can cause physiological disturbance, particularly to those subject to epilepsy. The flicker susceptibility of incandescent lamps is evident from the 3.45 exponent of EQ.3. High quality electronic fluorescent ballasts and LED drivers reduce lighting flicker in the process of operating the lamp at a constant power level regardless of mains voltage variations. Toward this end, they provide a desirable function. However, converting a significant portion of the lighting load to use constant power electronic fluorescent ballasts, and LED drivers, could cause the power grid to fail.
FIG. 5 presents the suppressed carrier impedance of a dual 20 Watt T12 fluorescent light that employs a typical older style inductive ballast. The near-zero phase angle shown in the data indicates that the impedance has a positive resistance positive damping quality at all modulation frequencies up to and beyond 30 Hz. The positive damping provided by this particular inductive ballast fluorescent light is approximately 1.5 times that provided by a Watt equivalent resistor of 447 Ohms.
FIG. 6 presents the suppressed carrier impedance of a 28 Watt T5 fluorescent light employing an Advance Inc. Centium ICN-132-MC high power factor electronic ballast. The near-180 degree phase angle in the low frequency data indicates that the impedance has a negative-resistance negative-damping quality in the modulation frequency band below approximately 3 Hz that includes the frequencies of concern involving oscillatory instability of the power grid. Examination of currently available LED driver controllers indicate that they are intended to operate in a constant power mode that would produce negative resistance negative damping qualities similar to those shown in FIG. 6.
Induction motors consume approximately half of the energy produced in the United States. When operated by direct connection to the power line, induction motors have a constant-power characteristic. For a given motor load, output power is determined primarily by motor shaft speed, which is determined primarily by mains frequency. Shaft speed varies little with mains voltage.
FIG. 7 presents the wye form phase to neutral suppressed-carrier impedance of a one horsepower three-phase induction motor driving a load that causes the motor to consume 200 Watts of input power at a reduced 49.1 Vrms line-to-neutral voltage. At low frequencies, the phase angle of the impedance is approximately −180 degrees, thereby confirming that the induction motor has a negative-resistance input impedance. The negative-resistance negative-damping characteristic exists for modulation frequencies below approximately 2.5 Hz. With an input power of 66.7 Watts per phase, the magnitude of the line to neutral impedance is predicted to be −36.1 Ohms by the constant power law of EQ.1. At 0.2 Hz, FIG. 7 indicates a value of 31.1956 dB//Ohm, or −36.3 Ohms that is in close agreement with the predicted value.
In a very large portion of motor applications, substantial energy savings can be obtained by operating motors as variable-speed drives (VSD). As an example, a ventilation fan operating at eighty percent of full speed consumes only fifty percent of the energy required to operate at full speed. With a variable-speed drive, motor speed can be adjusted to provide the optimum mechanical energy to perform the assigned task, rather than being cycled in a full-speed, zero-speed manner. The potential energy savings provide a strong economic incentive to employ variable-speed drives in applications wherein constant speed is not required and the economically optimum speed varies widely with the existing conditions.
Although operating induction motors via variable speed drives can provide a substantial improvement in efficiency, the impedance presented to the power line continues to have a negative resistance negative damping quality. If the drive output frequency and voltage applied to the motor remains fixed under varying line voltage conditions, the VSD would approximate a constant power load.
FIG. 8 and FIG. 9, respectively, present the suppressed carrier impedance of an unmodified Boston Fincor ACE-KL 2 hp VSD operating in “constant torque” and “fan-pump” mode. The low-frequency impedance values are higher than those expected from constant power operation. Maintaining a drive frequency at its programmed value would appear to be a simple task. In principle, constant torque mode requires that the voltage applied to the motor be increased in proportion to the programmed frequency. The proportional voltage compensates for the proportional back emf produced by proportional motor shaft speed resulting from the programmed frequency. The proportional voltage is required to maintain a fixed motor current, wherein the current determines the motor torque. In the interest of cost reduction, the VSD design may simply employ pulse width modulation of the rectified mains voltage to generate the motor voltage. Under the assumption that the mains voltage remains approximately constant, the pulse width would be increased in proportion to the programmed frequency. In this scenario, motor torque would be a function of mains voltage, thereby causing an alteration of the constant torque intent. The constant power characteristic would also be altered. In variable torque mode, such as used for driving fans, the motor voltage is varied exponentially with programmed drive frequency. The constant power characteristic would be altered to a greater extent.
The power grid has an ever-increasing tendency to become unstable and oscillate. The oscillation is in the form of low frequency torque oscillation of the rotating generator shafts. Although these oscillations begin at very low levels, they can quickly grow to levels that are highly disruptive and destructive. These oscillations are generally characterized in three distinct forms: inter-area, local mode and inter unit. Inter-area oscillations involve groups of generators that are located in widely separated geographical areas that are connected by very long transmission lines. These groups of generators oscillate in opposition to each other. Local-mode oscillation involves one or more generators, in a given geographical area, that are connected to the power grid by a common transmission line. These generators oscillate in unison against an otherwise stable power grid. Inter-unit oscillation involves oscillation between opposing units, or groups of units, in close proximity to each other, that are connected to the power grid by a common transmission line. Inter-area oscillation tends to occur in the frequency range of 0.1 to 0.5 Hz. Local-mode oscillation tends to occur in the frequency range of 0.7 to 2.0 Hz. Inter-unit oscillation tends to occur in the frequency range of 1.5 to 3.0 Hz. The length of the transmission line is a major factor in determining the frequency of oscillation. Heavy loading of the generators and transmission line tends to increase the likelihood of oscillatory instability. Inter-area oscillations tend to be the most troubling because they involve enormous levels of power and the situation is more complex because of the large number of generators involved. Local Mode oscillations are a frequent problem that may limit the amount of power that can be transmitted over the interconnecting transmission line. Inter Unit oscillations have been observed, but do not appear to be a major concern relative to the other two forms.
When the margin of stability is small, as is frequently the case, load fluctuations and switching transients produce damped sinusoidal perturbations of the grid voltage. Wavelet analysis of these damped sinusoids can be used to evaluate the degree of damping and thereby obtain an estimate of the margin of stability. Damping of 5 percent or less is considered to be cause for concern. Damping of 3 percent or less is considered to be cause for remedial action, involving dispatch of additional generation resources or rerouting of power transmission, to the extent that such options are available, or load shedding. With damping of zero percent, the sinusoidal perturbations do not decay. If net damping becomes negative, the oscillations can grow to dangerous and destructive levels. A negative damping situation demands immediate action that may involve emergency load dumping to avoid collapse of the power grid or a wide area blackout. Generators experiencing torque oscillation may be disconnected from the power grid to self-protect from damage. The resulting loss of generation capacity tends to exacerbate the situation and may produce a domino effect resulting in a wide area blackout.
The Synchrophasor system, currently under development, is designed to monitor power grid damping, synchronization, power flows and other parameters at a multitude of points on the power grid over the entire geographical area. Information thus obtained will be used by the Smart Grid to optimize power grid performance, thereby providing a major improvement in the ability to properly manage the power grid. Conceptually, the Synchrophasor system can process the collected data and derive control signals to be sent to the individual generators to cause them to react in a manner that opposes oscillation. In this mode, the Synchrophasor system would function as a Power System Stabilizer (PSS) for the entire power grid. Such a feature appears to be attractive. However, if the national power grid becomes dependent upon such a system in order to remain stable, this feature would be dangerous because centralization of stability control would create single-point-of-failure mechanisms. For example, the Synchrophasor system is dependent upon the Global Positioning System (GPS) for time synchronization. Momentary loss of the GPS would trigger massive oscillatory instability resulting in collapse of the power grid. The power grid needs to have a larger degree of inherent stability.
What is needed in the art is a method and apparatus for controlling an electrical load exhibiting destabilizing negative resistance negative damping characteristics to provide positive damping of power grid oscillations and for controlling the electrical load to operate at a reduced power level when the power grid voltage is reduced.